A generalized mathematical description for comparative assessment of various horizontal polar tube geometries with regard to external film condensation in presence of non-condensable gases

A generalized mathematical treatment is postulated to investigate the condensation heat transfer performance of horizontal tubes with varying geometries, with the presence of non-condensable gases in the free stream. The governing equations of mass, momentum and energy conservation in the liquid phase are solved semi-analytically, with matching constraints being imposed at the liquid-vapour interface, while the governing equations of energy and species conservation in the vapour phase are solved numerically. An air-water vapour system is considered for demonstrating the mathematical model. Special cases of the model are illustrated with the aid of elliptical and equiangular spiral geometries. It is revealed that the geometrical features of typical polar surfaces can turn out to be favourable in arresting probable drastic reductions in the condensation heat transfer rates that could be otherwise associated with the presence of non-condensable gases in the free stream. The favourable effects induced by polar surfaces become relatively more prominent, as percentage of non-condensable gases in the free stream increases. A geometrical shape function is also ascertained in this regard, which quantifies the extent of this augmentation in the heat transfer performance. In general, it is suggested that polar surfaces with higher values of the shape function over a majority of the azimuthal regime can turn out to be more desired choices for achieving enhanced rates of condensation heat transfer, provided that there are no serious manufacturability constraints.